Local Regression and Likelihood by Clive Loader

Author:Clive Loader [Loader, Clive]
Language: eng
Format: epub, pdf
Published: 2011-02-19T05:00:00+00:00

=

Pλ(y − 1) − Pλ(y) d P

dλ λ(Y ≥ y)

=

Pλ(y − 1). Use these relations to show

d2

dλ2 log Pλ(Y ≥ y) ∞

1

=

(P P

λ(y − 2)Pλ(j) − Pλ(y − 1)Pλ(j − 1)) .

λ(Y ≥ y)2 j=y

Hence show log Pλ(Y ≥ y) is a concave function of λ. Derive a similar expression for d2

dθ2 log Pλ(Y ≥ y) under the log link θ = log(λ), and again show this is concave.

7.6 For the cricket batting dataset from Example 7.6, estimate and plot the hazard rate. Use a local log-linear model with smoothing parameter α = 0.4 or smaller. Observe that the hazard rate displays an initial sharp decrease and then remains fairly constant.

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